A company is expected to have earnings of $3.64 per share next year, $4.1 in two

Question

A company is expected to have earnings of $3.64 per share next year, $4.1 in two years, and $5.16 in three years. The dividend payout ratio is expected to remain at 20% over the next three years. You estimate the risk-free rate to be 4% per year and the expected market risk premium to be 5% per year. In two years, you expect the lagging PE ratio to be 20. The beta of the stock is 1.3. What would be an appropriate estimate of the stock price today? (Answer to the nearest penny, i.e. 55.55 but do not use a $ sign).

Explanation / Answer

Step 1: Calculate Required Return (CAPM)

The required return can be calculated with the use of following formula:

Required Return = Risk Free Rate + Beta*Market Risk Premium

Using the values provided in the question, we get,

Required Return = 4 + 1.3*5 = 10.50%

__________

Step 2: Calculate Growth Rate with the Use of Lagging P/E Ratio

The formula for Lagging P/E Ratio is given below:

Lagging P/E Ratio = (Dividend Payout Ratio)*(1+Growth Rate)/(Required Return - Growth Rate)

Substituting values in the above formula, we get,

20 = (20%)*(1+Growth Rate)/(10.50% - Growth Rate)

Rearranging Values, we get,

20*(10.50% - Growth Rate) = .20 + .20Growth Rate

2.1 - 20Growth Rate = .20 + .20Growth Rate

Growth Rate = (2.1 - .20)/(20+.20) = 9.41%

__________

Step 3: Calculate Stock Price Today

The stock price today can be calculated with the use of following formula:

Stock Price Today = D1/(1+Required Return)^1 + D2/(1+Required Return)^2 + D3/(1+Required Return)^3 + D3*(1+Growth Rate)/(1+Required Return)^3*(Required Return - Growth Rate)

D1 = 3.64*20% =.728

D2 = 4.1*20% =.82

D3 = 5.16*20% = 1.032

Using these values in the above formula for stock price, we get,

Stock Price Today = .728/(1+10.50%)^1 + .82/(1+10.50%)^2 + 1.032/(1+10.50%)^3 + 1.032*(1+9.41%)/(10.50% - 9.41%)*(1+10.50%)^3 = $78.87

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